Empirical Characteristic Function in Time Series Estimation

Abstract

Since the empirical characteristic function is the Fourier transformation of the emipirical distribution function, it retains all the information in the sample but can overcome difficulties arising from the likelihood. This paper discusses an estimation method using the empirical characteristic function for stationary processes. Under some regularity conditions, the resulting estimators are shown to be consistent and asymptotically normal. The method is applied to estimate Gaussion ARMA models. The optimal weight functions and estimating equations are given for in detail. Monte Carlo evidence shows that thc empirical characteristic function method can work as well as the exact maximum likelihood method and outperforms the conditional maximum likelihood method.